Error Characterization of the Alpha Residuals Emissivity Extraction Technique Michael C. Baglivio, Dr. John Schott, Scott Brown Center for Imaging Science.

Error Characterization of the Alpha Residuals Emissivity

Extraction Technique

Michael C. Baglivio, Dr. John Schott, Scott Brown

Center for Imaging Science

Rochester Institute of Technology

Overview

• Hypothesis

• What’s the significance of this study?

• What is an Alpha Residual?– How does it work?

• Data sets

• Results

• Conclusion

Hypothesis

• The error associated with Wein’s approximation in the Alpha Residuals emissivity extraction technique can be characterized as a function of temperature and applied to real imagery.

Significance

• Algorithm assigns emissivity to each pixel of image

• Knowledge of spectral characteristics aids in material identification– pollution control– military vehicles– agriculture

What is an Alpha Residual?

• yields approximation to shape of emissivity spectrum

• one per spectral channel

• equations derived from Wein’s Approximation which is believed to be source of error

Alpha Residual from real data

X L

X L

X X

i i i

i i

i i i

ln

ln

Alpha Residual from library data

• Now take average of Xi spectrum to compute:

Ci i i i i i i ln ln ln ln1 5X

X Xi i i

C hc Cchk1

222 and

C

T2

How does it work?• Alpha Residuals computed for each channel of real

input data and library data

• iterative process that operates on 1 pixel – computes Alpha Residual for all library emissivity spectra– each library Alpha Residual spectrum then compared to

real input Alpha Residual spectrum– a pixels emissivity spectrum assigned to library

emissivity which yields spectrum most similar to real input alpha residual

Data Sets

• Frequency – Simulated emissivity curves generated

• cosine waves of varying frequency

• Sampling and spectral response– different numbers of sample points per channel

varied along with width of gaussian spectral response curve

Simulated Input Emissivity

0.94

0.95

0.96

0.97

0.98

0.99

1

1.01

0 50 100 150index

emis

sivi

ty

0.20.10.05

Error of Simulated Emissivities

-0.025

-0.02

-0.015

-0.01

-0.005

0

260 270 280 290 300 310 320 330

temperature [K]

erro

r [%

]

0.20.10.05

Analysis

• Low frequency emissivity spectra produce a slightly greater error relative to mid and high frequency spectra. Considering the change is over such a small region however, the difference is insignificant and frequency effects are negligible.

Real Input Emissivities

0.8

0.82

0.84

0.86

0.88

0.9

0.92

0.94

0.96

0.98

1

7.3 8.3 9.3 10.3 11.3 12.3 13.3 14.3 15.3

wavelength [microns]

emis

sivi

ty

arroyo

burnt paint

malpai

Error of Real Input

0.43

0.44

0.45

0.46

0.47

0.48

0.49

0.5

260 270 280 290 300 310 320 330

temperature [K]

erro

r [%

]

arroyo error

burnt paint error

malpai error

Average Error for Each Material

0.46665

0.4667

0.46675

0.4668

0.46685

0.4669

0.46695

0.467

0.46705

0.4671

0.46715

0.4672

average error

erro

r [%

]

arroyoburnt paintmalpai

Spectral Error Averaged Over Temperature

-2.00E-01

0.00E+00

2.00E-01

4.00E-01

6.00E-01

8.00E-01

1.00E+00

0 20 40 60 80 100 120

band

em

issiv

ity/e

rro

r

average

malpai

Analysis

• The difference between the material with the greatest error and the least error is 0.000328. Again, the error from material to material is negligible, telling us the algorithm will provide acceptable results regardless of what we’re looking at. Error is independent of emissivity magnitude.

Relationship of Samples Points to Response Width

• Relative width of spectral response function of the number of sample points input by user

1 2 3 4 5Sample points1

sample points: 1

response width: 3

sample points: 5

response width: 7

Effect of Sample Points on Total Error

0.43

0.44

0.45

0.46

0.47

0.48

0.49

0.5

270 280 290 300 310 320

temperature [K]

erro

r [%

]

3_75_7

Effect of Response Width

0.4

0.41

0.42

0.43

0.44

0.45

0.46

0.47

0.48

0.49

0.5

270 275 280 285 290 295 300 305 310 315 320

temperature [K]

erro

r [%

]

3_5

3_7

3_9

Comparison of the Two Effects

0.466

0.4665

0.467

0.4675

0.468

0.4685

1 3 5 7 9sample points/response width

erro

r [%

]

samplesresponse width

Analysis

• The three previous graphs show us that error has a direct relationship with response width and an inverse relationship with sample point. If you take more sample points, the error will be less but your making a sacrifice with respect to run-time.

Spectral Difference of Alpha Residuals

-2.50E-05

-2.00E-05

-1.50E-05

-1.00E-05

-5.00E-06

0.00E+00

5.00E-06

1.00E-05

1.50E-05

2.00E-05

1 11 21 31 41 51 61 71 81 91 101 111 121

band #

dif

fere

nce

270 K

280 K

290 K

300 K

310 K

320 K

Analysis

• By adjusting the alpha residual spectrum from the real input by the inverse of the values on the previous graph, the results yielded would be more accurate.

Conclusion

• error reduced by 0.5%

• high spectral resolution sensors increase accuracy

• general error correction can be applied to any image due to the negligible amount of difference in error between materials

THE END

Any Questions?